Abstract

Networks of coupled dynamical systems exhibit many interesting behaviours such as spatio-temporal chaos,
pattern formation and synchronization. Such networks can be
used to model a large variety of biological and physical systems. This contribution will focus on the 2-dimensional nonlinear map that describes the behaviour of individual neurons. The aim is to understand the coupling behaviour of this particular map and the dynamics of such coupled neuron systems. Various coupling schemes such as nearest neighbor coupling, random couplings and small-world networkings are numerically investigated. In particular, the paper will examine the transition of asynchronously firing neurons to a synchronous state. This is important in that it has similarities to the perceived behaviour of neurons in individuals during epileptic seizures.